Introduction to Combinatorics

Introduction to Combinatorics [May 01, 1972] Berman, Gerald Introduction to Combinatorics focuses on the applications, processes, methodologies, and approaches involved in combinatorics or discrete mathematics. The book first offers information on introductory examples, permutations and combinations, and the inclusion-exclusion principle. Discussions focus on some applications of the inclusion-exclusion principle, derangements, calculus of sets, permutations, combinations, Stirling's formula, binomial theorem, regions of a plane, chromatic polynomials, and a random walk. The text then examines linear equations with unit coefficients, recurrence relations, and generating functions. Topics include derivatives and differential equations, solution of difference equations by means of generating functions, recurrence relations, summation method, difference methods, combinations with repetitions, solutions bounded below, and solutions bounded above and below. The publication takes a look at generating functions and difference equations, ramifications of the binomial theorem, finite structures, coloring problems, maps on a sphere, and geometry of the plane. The manuscript is a valuable reference for researchers interested in combinatorics. Introductory Examples -- Permutations And Combinations -- The Inclusion-exclusion Principle -- Linear Equations With Unit Coefficients -- Recurrence Relations -- Generating Functions -- Some Methods Of Proof -- Geometry Of The Plane -- Maps On A Sphere -- Coloring Problems -- Finite Structures -- Probability -- Ramifications Of The Binomial Theorem -- More Generating Functions And Difference Equations -- Fibonacci Sequences -- Arrangements. [by] Gerald Berman And K. D. Fryer. Includes Bibliographical References.